中文摘要：

构造出1种递推的Kantorovich型算子,研究了其在LP（P〉1）空间上的收敛性和逼近特征,借助Hardy-Littlewood极大函数和Jensen不等式给出了该算子更加精细的逼近度估计,进而利用Lp空间中K-泛函和积分连续模的等价性获得了该算子的收敛阶为O（1/n（1/2））.

英文摘要：

A kind of recursive Kantorovich type operators is constructed. The convergence for these operators and ap- proximation characteristics on Le （P〉 1） space are studied. Then more sophisticated estimation of degree of approximation is obtained with using Hardy-Littlewood＇s maximal function and Jensen＇s inequality. At the same time, the order of convergence is characterized by 1√-n- with the help of the equivalence of K-functional and odulus of integral continuity on Le space.